help-13

[crimson sedge]

6/5 Jesus I’m bad at mental math

Negative

[gaunt hamlet]

I am too

[gaunt hamlet]

Yep, although 4/6 can be simplified

[crimson sedge]

11 2/3s

[gaunt hamlet]

And what about x?

[crimson sedge]

X = 37 1/3

[gaunt hamlet]

If x=(4/5)y, how could x be bigger than y?

[crimson sedge]

What did I do wrong

I plugged it into the x-2y-14 equation

[gaunt hamlet]

Can I see your work for that?

[gaunt hamlet]

So you got x + 70/3 = 14?

Or x - 70/3 = 14?

[crimson sedge]

Sorry the plus sign was just there

[gaunt hamlet]

The 2 is negative, and so is y, so the product should be positive

[crimson sedge]

Jesus

X is -9 1/3

[gaunt hamlet]

Yep

[crimson sedge]

Plug those in and I get my minimum?

[gaunt hamlet]

Hopefully

[gaunt hamlet]

[crimson sedge]

I just wasted my time

That 2y

In the lambda function

Is supposed to be positive

I’m an idiot

[gaunt hamlet]

Tbf I didn't see it either

We're both idiots

[crimson sedge]

Haha this is the shit that always screws me over missing positives and negatives and stuff like that

[gaunt hamlet]

But look on the bright side, you understand the process to doing this now hopefully

You learned how to solve a system of three equations

That's worth something

Not points unfortunately

But something

[crimson sedge]

Yeah haha that’s the main thing

I’m gonna workout it again and see if I get it right this time

Ok so we got the x and y value right

Confused on how to get the minimum value

[gaunt hamlet]

You just have to plug them back into f

[crimson sedge]

I did

[gaunt hamlet]

Can I see?

[gaunt hamlet]

4² times 5²?

[crimson sedge]

I warned u

[gaunt hamlet]

Lol

[glossy halo]

ummm, "308" vs "380"?

[crimson sedge]

Haha thanks for the help man

[glossy halo]

And what Dio said haha

[crimson sedge]

Jesus it gets worse

How would a maximum work?

Same process?

[gaunt hamlet]

But hey, at least you understand the concept. All your errors are evaluation errors, not conceptual errors

It's the exact same process, yes

[crimson sedge]

So it’s based on the constraint that it’s a minimum or maximum?

[gaunt hamlet]

The constraint and the function. There's something called a bounded hessian (or sumn like that) which will tell you if you have a max or min, but all your problems will tell you beforehand which it is so don't worry about that for right now

[crimson sedge]

Ah alright cool

One last thing

[gaunt hamlet]

*bordered hessian

What's the last thing?

[crimson sedge]

How would u use the >

Would the first function be to maximize and the second fuctikn to minimize?

[gaunt hamlet]

No, you should use both at the same time

Let me check my textbook

Fuck, my textbook doesn't cover inequalities

Do you have any notes on the subject?

[crimson sedge]

Nope it’s not even in the textbook

She didn’t show a single one in class so I doubt it’s gonna be on the test

[gaunt hamlet]

Maybe just solve the problem as if it was only x² + y² = 8. I'm imagining the inequality will come in later

[crimson sedge]

Yeah that’s a good idea

If it’s wrong I’ll figure something else out

Thanks for the help man

[gaunt hamlet]

Np

I just worked out the problem, it should work, although you can't use the elimination method from before

[crimson sedge]

Substitution right?

What happens with the inequality

[gaunt hamlet]

Yeah, substitution

You will, or at least I did, end up with something of the form x² = a. Knowing x > 0 let's us know whether x is √a or -√a

[cedar kiln]

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[crimson sedge]

Bet thank you

[cedar kiln]

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[vivid saffron]

Im doing a test review and it says to solve each linear system by substitution and i dont know how to do this can anyone help?

[livid hound]

would you be able to solve a simpler system like
$$\begin{cases} y = x + 2 \
3x + 7y = 24 \end{cases}$$
using substitution?

[wraith dagger]

ℝamonov

[vivid saffron]

I think i can do that yeah but i havent got a lot of practice

[livid hound]

how would you do this one?

[vivid saffron]

I would plug x + 2 for y in the second equation

and then um

combine like terms

and then subtract the 2 and add it to 24

and then i'd divide both sides by 10 and get 22/10 i think

[livid hound]

is not correct

[vivid saffron]

oh

[livid hound]

you're not substituting and/or expanding properly

[vivid saffron]

how do you do it correctly ?

[livid hound]

when substituting here, you should use sufficient parentheses so that 7 is still being multiplied to whatever y is

$3x + 7\red{(}x+2\red{)} = 24$

[wraith dagger]

ℝamonov

[vivid saffron]

ohhhhh

oops i forgot to multiply 7 by 2

sorry its hard to do it mentally in my head

[livid hound]

don't do it in your head

write it out

[vivid saffron]

oh ok

so x is equal to 1 right

[livid hound]

yes

[vivid saffron]

oh ok

so wait then how would i do

this one

[livid hound]

well note that in the simpler example, one of the variables was already isolated, allowing you to perform a substitution immediately

consider isolating a variable in one of your equations

it doesn't really matter which, but ideally choose the one that would require the less work

[vivid saffron]

oh okay

how do I know which one will require less work ? sorry im a bit slow with this type of stuff

[livid hound]

you should have a decent idea of what isolating a certain variable would involve

e.g. what sort of stuff does it look like you'd need to do to isolate x in the first equation

[vivid saffron]

ah idk like multiply it by 3 or something

and then add the 1 to the 11 ?

[livid hound]

rid yourself of fractions, multiple steps of addition, subtraction
and probably still end up with fractions at the very end after isolating x

and compare that to something like isolating y in the second equation

[vivid saffron]

ohhh yeah you're right

it makes more sense now

I was just looking at it brain dead or somtehing i dont know why i couldnt understand that

[livid hound]

although for the first equation you would still

rid yourself of fractions
when solving

[vivid saffron]

oh okay

so y = -16 + 2x?

[livid hound]

yes

[vivid saffron]

the hard part for me is subbing that into the first equation and trying to solve it

I forgot everything i learned in 9th grade lol

[livid hound]

before substituting, consider first

rid yourself of fractions
(in the first equation)
(by multiplying both sides of the equation by the lcd (lcm of the denominators))

[vivid saffron]

so 6?

[livid hound]

yes

[vivid saffron]

that gets rid of all the bottom denominators???

[livid hound]

yes

[vivid saffron]

ohh

[livid hound]

it'll be more convenient if you explicitly use 2 * 3

[vivid saffron]

so its

wait a sec

x - 1 + 32 - 4x + 4 = 66?

and then i find x?

i got 31/3 im probably wrong

[livid hound]

you're not multiplying properly

[vivid saffron]

oh oops

[livid hound]

and actually looking closer

2(y-2)/2 can be simplified to (y-2)

so multiplying both sides of the equation by 3 is sufficient

[vivid saffron]

ohhh

[livid hound]

and note that if multiplying both sides by 6,
you're supposed to be multiplying each entire side by 6

NOT one term by 3 and another by 2

[vivid saffron]

are you saying the top of the fraction hsa to be multiplied by 6 as well

sorry im so dumb rn cuz im on like 3 different drugs from srgery

[livid hound]

multiplying both sides by 6
$$6\br{\frac{x-1}{3} - \frac{2(y-2)}{2}} = 6 \cdot 11$$

[wraith dagger]

ℝamonov

[vivid saffron]

oh wth

so it would be 6x - 6/3 - 12(6y - 12)/2 ?? ahh

[livid hound]

supposedly you did something like
$$3\cdot \frac{x-1}{3} - 2\cdot \frac{2(y-2)}{2} = 2 \cdot 3 \cdot 11$$
which is NOT multiplying both sides by 6

[wraith dagger]

ℝamonov

[vivid saffron]

oh oops i was doing that

[livid hound]

6x - 6/3 - 12(6y - 12)/2
no

missing parentheses and multiplication doesn't distribute over multiplication

a(bc) isn't ab * ac

a(bc) = abc

[vivid saffron]

oh okay

[livid hound]

also note the reason why 6 was chosen, you don't need to explicitly expand the product of 6 and the numerators

[vivid saffron]

ohh

how old are you? you seem very smart and good at teaching

I got y = 20 and x = 18 is that right @livid hound

I plugged the numbers in the second equation and it worked but photomath is saying its (4, -8)

[livid hound]

(4,-8) is the correct solution

have you done the work on paper?

can you take a pic

[vivid saffron]

yes okay

I didnt know i was gonna take a picture so you might be confused when reading it

cause im confused reading it

[livid hound]

assuming the stuff on the bot right is supposed to be the updated work

you didn't perform the division and subtraction properly, nor did you distribute the 6 to that term

[vivid saffron]

oh oops

[livid hound]

you also seem to by misinterpreting what 2(-16 + 2x - 2) represents

[vivid saffron]

yeah its confusing me

[livid hound]

2(-16 + 2x - 2) represents the product of 2 and (-16 + 2x - 2)

and the simplification of 2(-16 + 2x - 2)/2 should be relatively simple

how would you simplify something like
$$\frac{2 \times 57894327}{2}$$

[wraith dagger]

ℝamonov

[vivid saffron]

Id multiply the 2 x 57894327 and then divide it if i can?

[livid hound]

bad idea

[vivid saffron]

oh wait really why

[livid hound]

$$\frac{123456789}{7} \cdot \frac{5}{987654321}\cdot \frac{987654321}{123456789}$$
there is absolutely no need to explicitly multiply those numerators and denominators together to get:
$$\frac{609663155563176345}{853528417788446883} = \frac57$$

[wraith dagger]

ℝamonov

[vivid saffron]

oh jeez

[livid hound]

when you can just consider the commutative property of multiplication:
$$\frac{123456789}{7} \cdot \frac{5}{987654321}\cdot \frac{987654321}{123456789} = \underbrace{\frac{123456789}{123456789}}{1} \cdot \underbrace{\frac{987654321}{987654321}}{1}\cdot \frac57 =\frac57$$

[wraith dagger]

ℝamonov

[vivid saffron]

those numbers turned into 5/7? what thehell

LOL Im so bad at math oh my god

[livid hound]

$\frac{2 \times 57894327}{2} = \frac22 \times 57894327 = , ?$

[wraith dagger]

ℝamonov

[vivid saffron]

wont it just become the same number

[livid hound]

wdym

[vivid saffron]

the 2/2 x 57894327

[livid hound]

simplifies to...?

[frosty oxide]

2/2 equals to 1

[obsidian coral]

That's the point ramonov was proving, without saying that

[vivid saffron]

1 x 57894327 equals 57894327 ?

[livid hound]

yes

and the same principle can be applied to simplify

2(-16 + 2x - 2)/2

the stuff inside the parentheses can also be simplified

[vivid saffron]

can you show me how you would simplify that

[livid hound]

more or less the same way the stuff with numbers was simplified above

[vivid saffron]

ah

[frosty oxide]

since you're multiplying by 2, and then dividing by 2, it cancels out

[vivid saffron]

do you mean like this?

[livid hound]

yeh pretty much

[vivid saffron]

ohh

sorry for all the annoying math questions i shouldnt be struggling over this but i havent done math in like 2 years

ill stop bothering everyone now

[cedar kiln]

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[light void]

How can you easily put it into brackets

[gentle lintel]

wdym brackets

[light void]

It is differentiation from fir principles

[bold vine]

Not sure what “first principles” is

[livid hound]

limit definition

[bold vine]

Oh okay

[cerulean star]

"First Principles" = Difference Quotient or epsilon-delta?

[bold vine]

Limit definition of a derivative

[gentle lintel]

wdym by brackets?

[cerulean star]

Ok well those are all just polynomials

[livid hound]

qhats your issue with parentheses

[light void]

The highlighted bit

[cerulean star]

The derivatives of polynomial types fall out of the difference quotient like turds out of a horse

(Almost no effort)

[light void]

Like I don't know how to put them

[gentle lintel]

uhh

[livid hound]

still not sure what exactly you're trying to type

[gentle lintel]

that’s quite terrible presentation

don’t mind the parentheses

[light void]

Ok so how can I turn this

[bold vine]

What you’re doing looks slightly different than the limit definition of a derivative

But it looks like it works

[light void]

Into this

[gentle lintel]

this is just one way to present the proof

(which in my opinion is bad)

[bold vine]

I believe this is how most people know the limit definition

[light void]

So how does that work?

[bold vine]

You can use this for your problems

[bold vine]

It comes from the idea of moving one point infinitely close to another to approximate the slope at some point

For more visual representations of this, I recommend 3Blue1Brown’s Essence of Calculus playlist

[cerulean star]

@light void just do the function with "x+h" plugged in and with "x" plugged in, do all the parts, take the limit as h goes to 0

There isnt any fancy stuff to do with polynomials

[bold vine]

^^

[cerulean star]

The h's that would cause problems factor out

[bold vine]

There will be some algebra involved, but absolutely doable

[cerulean star]

That's why its easy

[light void]

Alright

[light void]

I will watch that as well

Thanks

[bold vine]

It’s on YouTube 🙂

Just in case

[cerulean star]

Yeah, just watch an example on youtube

^

[light void]

Damn that is easy with this method

Otherwise I would be on it for hours

Thanks guys

[bold vine]

Np 🙂

Close the channel if you’re done

[light void]

.close

[cedar kiln]

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[wide forge]

i need help in this, dont know how to do it

[bold vine]

Create auxiliary lines from the center to where the chord meets the circle

[livid hound]

start by drawing a diagram

[bold vine]

^^

[wide forge]

auxiliary ?

[bold vine]

Sorry - those are lines that you draw/add to the diagram

They can allow you to see certain relationships more clearly

[wide forge]

ok, drew a diagram of radius 25cm, chord is 48cm, now what?

[bold vine]

Draw what you are looking for, and think about what information you have that you can use to get the piece of information you want

[livid hound]

draw in the shortest line from the centre to the chord

[bold vine]

^^

[livid hound]

and consider the special properties related to this line

[bold vine]

^^

[wide forge]

oh ok

[wide forge]

ok got it

[cedar kiln]

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[jolly forge]

find x,y

[crimson sedge]

factor

[jolly forge]

but how

[crimson sedge]

oh wait there is an xy term

uh, enjoy doing the quadratic formula with this

though there should be a simpler way i can't think of rn

[dire geode]

Probably faster to just use quadratic formula than to try to be clever

[bold hinge]

2 variables

one equation

Lol gl

[crimson sedge]

solve relative to each other

the answer isn't pretty, i've seen the work

[bold hinge]

ok great

[steel canopy]

Is that algebra? Seem like a lot of works.

[jolly forge]

yup

[bold hinge]

Let this be a polynomial in x and treat y as a constant then

[steel canopy]

When I took algebra. I learned to solve for x, y. That's about it.

[bold hinge]

Ok.

[dire geode]

,w solve 5x^2 + 9y^2-12xy +24x-48y+80=0

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[cedar kiln]

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[unreal sleet]

,tex 3^2^x × 3^3^x

[cedar kiln]

Please don't occupy multiple help channels.

[wraith dagger]

Space
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[unreal sleet]

do the 3 and 2 plus

[hollow osprey]

@unreal sleet what is your question?

[cedar kiln]

@unreal sleet Has your question been resolved?

[livid hound]

your tex is horrid, what's the original question supposed to be

[cedar kiln]

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[thick imp]

I believe you should also be given a side

[livid hound]

the instructions and setup are poor

its supposed to be given that you start with an equilateral triangle

did they have markings to indicate whether the triangle was equilateral?

or isosceles

[thick imp]

You can calculate each angle in the larger triangle as 60

[livid hound]

do you have an exact image of the figure?

or is the thing above an exact replica

was that marking around that supposed right angle curved?

was it shown like how you drew it, or was it

wdym the right angle was given

a curved marking doesn't indicate a right angle

[thick imp]

^

[livid hound]

if they had something curved, the diagram sucked

is curved

not rigid

[thick imp]

Its a curved angle, right angles are shown as squares

Oh

[livid hound]

ok

in that case, consider the construction from the dotted lines

and form an equilateral triangle

equilateral

the entire base will also have length a

yes

no

[wraith dagger]

Kepe

[livid hound]

yes

[wraith dagger]

Kepe

[livid hound]

wait

[wraith dagger]

Kepe

[livid hound]

answered too quick

you're missing parentheses

note that the side is a/2

and when you are applying pythagoras, you should be squaring a/2

[wraith dagger]

Kepe

[livid hound]

yes

[wraith dagger]

Kepe

Kepe

Kepe

Kepe

Kepe

[cedar kiln]

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[jaunty mural]

Note using an equilateral triangle with side length 2 will get you those angles easier, although working with the general case is fine.

[cedar kiln]

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[sonic wing]

(3*h)+89=h+z

[sonic wing]

z=

how can we simplify it??

[crimson sedge]

2h+ 89

[sonic wing]

I am only able to simplify it till : 2h+89=z

[crimson sedge]

Yeah thats what z is, we can’t simplify more than that

[sonic wing]

Ok thnks

.close

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[cedar kiln]

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[gray condor]

?

[cedar kiln]

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[atomic cipher]

Can someone dm me how to do questions like these? (Im going to bed and the bot will probably say it resolved automatically - thats y i asked for dm)

[foggy merlin]

,rotate

[cedar kiln]

@atomic cipher Has your question been resolved?

[cedar kiln]

@atomic cipher Has your question been resolved?

[flint siren]

use the rules to solve inequalities

your book will have them

[cedar kiln]

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[trail sail]

I'm learning about sparse Gaussian process, most of tutorials are talking about how to select the inducing points like how to maximum the probability of f given by inducing points. But I'm confused, after I have the inducing points, is that everything else will be same as normal GP? Like I just need to calculate the posterior with the inducing point instead of original data set?

[cedar kiln]

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[weak flare]

Hi im studying for exam but i got stuck on this question. can you give me a clear explanation? thanks.

[hoary notch]

Hint: ASA

[weak flare]

theres no s in the figure?

[hoary notch]

Are you learning congruency right now?

[weak flare]

oh no im not

im learning about triangles

[hoary notch]

Okay try to make a right triangle

[viscid hearth]

ASA means conguent by "angle side angle"

[hoary notch]

That incorporates DC

[weak flare]

ik

okayill try

oh i got it

lemme work out ill send a pcture of my working to check

is DC 25?

[hoary notch]

Yes

[weak flare]

oh ic i understand the working no need to explain, thanks for the help

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[wanton glacier]

why don't they just cancel them out?

[dense wing]

cause you don't have (b+1)/(b+1)

[wanton glacier]

so the numerator and the denominator on the LHS have to be the same in order for them to cancel out?

[dense wing]

a/a=1, yes

[wanton glacier]

oh wait, why did my instinct tell me to cancel them out instead of cross multiply lol

oh wait that's a stupid question I already knew it lol

rip

thanks

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[dense wing]

Write out CAB=BA given you know AB and BA

then compute CAB by defining the 4 variables to solve

yeah, now define C as [a,b][c,d]

then solve for a-d

yes.

,rotate

[dense wing]

yes

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✅

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[jaunty pike]

The following figure is completed by placing whole numbers in each box. If the number is in a circle-shaped box, it is obtained by subtracting the two numbers in the boxes directly below it. If the number is in a hexagon-shaped box, it is obtained by adding the two numbers in the boxes just below it. The 5 numbers on floor 1 are written so that the two numbers on the ends are odd. Prove that the number written in the upper box is always even.

[jaunty pike]

I mean, I get the problem, but how do I exactly prove that?

[jaunty mural]

Try a few examples of number placements

and see if you notice something

[stray olive]

maybe call the bottom 5 numbers a,b,c,d,e.
the hexagons above are then gonna be a+b,b+c,c+d,d+e. the circles above that will be (a+b)-(b+c)=a-c, (b+c)-(c+d)=b-d, and (c+d)-(d+e)=c-e, the hexagons above that will be (a-c)+(b-d) and (b-d)-(c-e), and the circle with be [(a-c)+(b-d)]-[(b-d)-(c-e)]=a-c+b-d-b+d+c-e=a-e

since a and e are odd, a-e is even.

[jaunty pike]

oh yea gotcha

[jaunty pike]

i mean yeah i two things

[stray olive]

sorry i had to edit some typos

[jaunty pike]

that my numbers are ugly af and that it always ends in an even number

[stray olive]

yep! cool huh?

[jaunty pike]

yea gotcha, thank you both!

[stray olive]

np

[jaunty pike]

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[crimson sedge]

given that n can be any integer such that n>1, prove that n^2-n is never an odd number?. im stuck on where to even start

[trim sentinel]

That seems easy

At least at first look

@crimson sedge i suggest prove even number squared - even number is always even number

Then prove odd number squared - odd number is even number

[crimson sedge]

how do i express an odd number in terms of n. i know how to do an even one

[trim sentinel]

$$2n + 1$$

[wraith dagger]

Pluton

[crimson sedge]

thank u

[crimson sedge]

i proved that its always an odd number lol i cant make a proof for it being even

[trim sentinel]

Umm

How

[crimson sedge]

one sec lemme show it

[trim sentinel]

You forgot the 2

Its 2n + 1

But i wouldnt prove it that way

[crimson sedge]

ohhhhh yeh sorry i forgor the two

but then i get 4n^2+3n+3, which cant be divided by two

[trim sentinel]

Well you did something wrong again

I see you did -n + 1

So i guess now you did -2n + 1

And it should he -(2n + 1)

[crimson sedge]

ohhhh yeh BRUH IM SO BAD AT THESE

ok so now ive done both of those proofs what do i do now

[trim sentinel]

Well did you prove it?

[crimson sedge]

i proved the two things u told me to prove at the beginning

[trim sentinel]

Then thats done

[crimson sedge]

then how do i solve the original question

[trim sentinel]

Well you did

You proved for any number it will be divisible by 2 therefore its even

[crimson sedge]

oh ok

on this website though its asking me to write it in terms of n^2-n=?

how would i express the ?, would i set the two equations equal to eachother and find n^2-n?

[trim sentinel]

I dont get what the website asks you?

[crimson sedge]

lemme take a screenshot

[trim sentinel]

I mean proving for all even and for all odd numbers you proved it for all integers

[trim sentinel]

Idk what the website wants from you

[crimson sedge]

fr its weird af

ill just skip the question its cool

[trim sentinel]

I mean you did prove it

I just dont know a way they want you to write the proof in

[crimson sedge]

exactly, strange

ill speak to my teacher abt it tomo

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[warm glacier]

In how many ways can Chris choose 3 gifts for his partner among 8 different articles?

[warm glacier]

So I know that the answer is 8C3 for combinations (whhich equals 56)

but why is it not 8x7x6?

[flint plinth]

8x7x6 assumes the ordering matters

If it does not matter then you need to divide by the number of possible orderings of the same items, which is 3!

And the result of that division is 8C3

[warm glacier]

Oh alright thanks

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[mental mesa]

I need help solving a problem trigonometry related

[mental mesa]

Would the lenght of x be correct

<@&286206848099549185>

[keen elbow]

are you using radians or degrees?

[mental mesa]

Idk

What’s difference

@keen elbow

It’s a degree

[keen elbow]

https://images.slideplayer.com/19/5824057/slides/slide_4.jpg

[mental mesa]

It’s degrees

It’s degrees I’m sure

Is it correct

@keen elbow

[crimson sedge]

you messed up your ratios cos is adj./hypotenuse, sin is opp.hypo. and tan is opp./adj.

[cedar kiln]

@mental mesa Has your question been resolved?

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[west wyvern]

Given the condition $\nabla^2 \Phi = 0$, the solution of the equation $\nabla^2 \Psi = k\vec{\nabla}\Phi \cdot \vec{\nabla} \Phi$ is...?

[wraith dagger]

idioticbaka1824

[west wyvern]

This feels like it should be simple, but for some reason I can't seem to find any way to proceed...

[trim sentinel]

Phi here is golden ratio?

[west wyvern]

ah, sorry, no, it's just a function of spatial coordinates

[cedar kiln]

@west wyvern Has your question been resolved?

[west wyvern]

I'm looking for \Psi as a function of \Phi

[cedar kiln]

@west wyvern Has your question been resolved?

[cedar kiln]

@west wyvern Has your question been resolved?

[cedar kiln]

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[formal nest]

a) asks why is the series not a taylor series centered at 1

b) is the same but for 2

can someone help me ?

Is it because of the positive/negative sign ?

[cedar kiln]

@formal nest Has your question been resolved?

[formal nest]

<@&286206848099549185>

[cedar kiln]

@formal nest Has your question been resolved?

[jaunty mural]

Recall the definition for taylor series

In particular what each term actually is

[formal nest]

Does it miss the n! Underneath?

@jaunty mural

Sorry for ping

[jaunty mural]

no...

$$\sum \frac{f^{(n)}(a)}{n!}(x-a)^n$$

[wraith dagger]

Shuri2060

[jaunty mural]

Do you understand that entire fraction is the coefficient?

it evaluates to a constant for each n

[formal nest]

yes

tbh i dont know what is missing

[jaunty mural]

Ok so

in the first one

what is f(1)

[formal nest]

1.6 ?

well not rly but

[jaunty mural]

why not really

[formal nest]

1.6 is the left over when you replace n by 0

[jaunty mural]

apply this definition directly

well yes?

the 0th derivative

is the function itself

[formal nest]

yhea

[jaunty mural]

so f(1) = 1.6 yes?

what is f'(1)

[formal nest]

i dont have a formula how could i know

[jaunty mural]

i gave you the formula, you should know.

[formal nest]

well

[jaunty mural]

$$T_a(x) = \sum^\infty_{n=0} \frac{f^{(n)}(a)}{n!}(x-a)^n$$

[wraith dagger]

Shuri2060

[jaunty mural]

Taylor for f centered on a

Now compare this to the series you are given

you should be able to figure out what f'(1) is

[jaunty mural]

if you dont like the summation, expand out the first few terms

[formal nest]

:c

i dont understand

everything seems normal except the minus maybe

[jaunty mural]

ok can you show me

what the first few terms of a general taylor should look like

from your notes or whatever

[formal nest]

i need a function to start from

[jaunty mural]

From expanding that summation out

[jaunty mural]

Have you never seen this???

[formal nest]

yes

usually the question would be expand the taylor series of cos(x) or ln(x) or whatever

then you can do stuff

idk

maybe im stupid

prob

[jaunty mural]

I am asking for the general taylor series

[formal nest]

yhea

[jaunty mural]

$$T_a(x) = \sum^\infty_{n=0} \frac{f^{(n)}(a)}{n!}(x-a)^n$$

[wraith dagger]

Shuri2060

[formal nest]

ok well

[jaunty mural]

In this form. Except you expand that summation

what do the first few terms look like?

[formal nest]

first term would be that formula but with all n replaced with 0

[jaunty mural]

well yes...

[formal nest]

seconds same thing but with 1

[jaunty mural]

yes....

[formal nest]

thrird with 2

[jaunty mural]

can you write this out?

[formal nest]

ig

[jaunty mural]

for yourself at least

[formal nest]

give me a sec

[jaunty mural]

Then compare this to the series given to you

because each of these terms should correspond to each other...

since its meant to be a taylor series centered on 1

[formal nest]

do i replace a with 1 ?

[jaunty mural]

Well yes

[formal nest]

ok

[jaunty mural]

They give you a series centered on 1

so a is 1

[formal nest]

yhea

[jaunty mural]

Next, you should be able to deduce any of the derivatives

that are given

you should be able to find
f(1)
f'(1)
f''(1)
f'''(1)

[formal nest]

like this ?

[jaunty mural]

yh ok

now look at what the question gives you

[jaunty mural]

to get these 4

[formal nest]

1.6-0.8(x-1)+0.4(x-1)^2...

f(1) = 1.6

f'(1)=0.8

f''(1)0.4

f'''(1)=0.1 ?

[jaunty mural]

how did you get f'' = 0.4

https://media.discordapp.net/attachments/903430334681608232/945095188584497233/image0.jpg

You also ignored the sign on 0.8

[formal nest]

yhea true

and i should multiply the values by the denominator

^ yes ?

[jaunty mural]

Like I said, the series are meant to be exactly the same

so +0.4 = f''(1)/2

yes?

[formal nest]

yhea

[jaunty mural]

Anyways, this is not what the question was asking for - it doesnt want all the derivatives. I got you to do this since you didn't seem to understand this point of the Taylor series.

The question just wants you to identify what is possibly wrong with some of these derivatives

[formal nest]

so how do we solve that

[jaunty mural]

I told you the idea - you find out.

[formal nest]

bruh

[jaunty mural]

Look at the graph, look at the derivatives.

Thats the only thing youve got.

[formal nest]

D:

is it because the fucntion is rising when its not supposed to ?

[jaunty mural]

yes

[formal nest]

...

[jaunty mural]

The 2nd one is harder, but try to figure it out.

[formal nest]

i just guessed

no way imma be able to find that out

[jaunty mural]

why the guess

you have the first derivative

You found it was negative in the first one

[formal nest]

cause u said to look at the graph and that the sign was important

[jaunty mural]

The first derivative was negative but the graph has positive slope

yes?

Now try to find the issue in the 2nd series

[formal nest]

but why is this true since the slope is affected by \ the sum of all the terms

[jaunty mural]

????????

For the first series

What is f'(1)

[formal nest]

the graph is true for the whole series

not just one term

[jaunty mural]

i have no idea what you mean

you are able to compute what f'(1) is yes or no

[formal nest]

the function represents the whole series

right ?

[jaunty mural]

i dont...

what is f'(1) in the first series

[formal nest]

-0.8 ?

[jaunty mural]

yes?

what is the slope of the graph at 1?

[formal nest]

positive

[jaunty mural]

yes?

[formal nest]

but but but

the fucntion is a series

[jaunty mural]

I.

whats your point

im missing what you re trying to say

[formal nest]

my point is for example the value of f(1) is the sum of ALL the terms of the series

no ?

[jaunty mural]

when you plug in x = 1

[formal nest]

yes

[jaunty mural]

alright.

and that is ...?

[formal nest]

so how does the little first derivative matter

[jaunty mural]

???????

you realise when u plug in x = 1

all of the terms die

[formal nest]

the first derivative is the second term of a BIG BIG BIG sum

[jaunty mural]

except for when n = 0

[formal nest]

why

[jaunty mural]

have a LOOK

at what the series is

[jaunty mural]

.

you wrote out part of it

[formal nest]

yhea

[formal nest]

i dont understand this statement

[jaunty mural]

what do you not get

[formal nest]

why do they die

[jaunty mural]

you plug in x = 1

and a = 1

(1-1)^n

[formal nest]

n will stil lgo from 0 -> inf

[jaunty mural]

on every term

thats otherwise known as 0

[formal nest]

hmmm

[jaunty mural]

but that isnt even relevant

to this question

the point is you can compute what f'(1)

is from the series you are given

it is negative.

[formal nest]

i think i dont understand how a series and a fucntion are linked togheter

[jaunty mural]

while the gradient is positive

Well I cant do much about that

Read some stuff online

[formal nest]

you can i believe in u

[jaunty mural]

/tutorials

about taylor

I dont even know what is the issue here

[formal nest]

me neither

[formal nest]

this

[jaunty mural]

you have (x-a)^n

[formal nest]

because the value of f(1) is the sum of all the terms when u plug x and a

[jaunty mural]

in every single term

well yes?

[formal nest]

yes

then

[jaunty mural]

so every term except for n = 0 will vanish

[formal nest]

how can the first derivative determine the whole slope

[jaunty mural]

urgh

You are relating unrelated things it seems to me

but maybe I misunderstand

try #calculus

[formal nest]

i need to understand them before resuming

[jaunty mural]

Try #calculus , I cannot make heads or tails of your muddle

[formal nest]

ill just skip this question and hope i dont need it for the exam

thx for the help tho

.close

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[dawn quail]

Hi, I wan't to learn how to transform canonical and factorised into polynomial form because i'm really struggling at this theme

[dense wing]

wdym

[dawn quail]

for example:

i wan't to transform it to polynomial form

[bright surge]

expand?

[bright surge]

expand the expression

[cedar kiln]

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[cedar kiln]

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[spice atlas]

Is this an octal number or is it something else?

[spice atlas]

what does that mean

[hoary notch]

Is this a test btw?

[obsidian coral]

Why is it 6 marks? Is that a test?

[spice atlas]

its an assignment

[obsidian coral]

It's homework?

[spice atlas]

yes

[obsidian coral]

Yes, 0 at the front is to denote as octal

[spice atlas]

do you guys know what number is this?

[obsidian coral]

0x is hexadecimal

[spice atlas]

okayy then

so the 0x is a hexadecimal

gotcha

[cedar kiln]

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[cedar kiln]

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[warped vortex]

When calculating the total sum of squares adn you're given the data in (x,y), do you only take into account the y value?

[bronze crag]

@warped vortex It depends on the context. Sometimes, you do interpolation, and calculate the dist to the line and square that

I guess it could also mean you take the sum of the dist to the average point (xbar, ybar)

[cedar kiln]

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[viscid hearth]

What are you stuck on?

Do you know how to find percentages?

Like x percent of 600 is 50?

What is it asking?

What’s the problem asking

Are you confused on what the problem is asking you or how to solve it? Or both?

[cedar kiln]

@crystal galleon Has your question been resolved?

[cedar kiln]

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[warm vector]

I used BODMAS but it didn’t work. I’m confused.

[warm vector]

I did this:
6(15-12+1)
6(15-13)
6(2)
12

[west wyvern]

6+(15-6*2+1)
6+(15-(6*2)+1)
6+(15-12+1)
6+(3+1)
6+4
10

[vale pike]

R u serious man

Man like, super easy

6+(15-12+1)
6+4=10

[warm vector]

But I did 12 +1 before

[vale pike]

It doesnt matter

Just do the multiplication

First

[warm vector]

Why though? Like why didn’t bodmas work?

[vale pike]

What’s bodmas?

Use photomath

[warm vector]

Ok

[vale pike]

The order of simple operations doesnt matter(addition and substraction)

[warm vector]

Then why is there a whole rule of bodmas

[vale pike]

It tells u the order

[warm vector]

Multiplication comes before addition and addition comes before subtraction

[warm vector]

Yh but I followed that order and didn’t get it

[vale pike]

That’s the order

[warm vector]

(15-12+1)

[vale pike]

At first u multiply

Because there is multiplication

In the parentheses

And then , u add up those numbers

[warm vector]

But referring to this, if we do 12+1 first and subtract we get something different

[vale pike]

After u did the multiplication

[warm vector]

We get 2

Instead of 4

[vale pike]

U should do the operations

From the left side

To the right

[humble sleet]

Pem/da/s

[warm vector]

Ok this is what I follow: brackets first, division, multiplication, addition and then subtraction

[vale pike]

No

If addition comes first

Then addition

Like

Multiplication and division

Are on the same level

[humble sleet]

When there is multiplication and division or subtraction and addition you do the operation that is left first

[vale pike]

Of importance

Whatever comes first u do

[vale pike]

Yeah, that’s what im talking about

[humble sleet]

M/D and A/S

They have the same importance classification so u do the left one first

Thats basic order of operation

[warm vector]

Wth was I taught bodmas then?

[vale pike]

It is the same

[cunning quail]

the main issue is just in (15-12+1) you did 12+1=13 when it should be -12+1=-11

[vale pike]

Oh yeah

I didnt notice that at first

Either

Yeah, kinda confused me

When additioning or subtracting

The order

[warm vector]

That’s what I did

[vale pike]

Doesnt matter

[vale pike]

.

U did 12+1

Instead of -12+1

[warm vector]

Ok yh I’m not alright I get it

[vale pike]

To get -11

[warm vector]

Yh I should probably die or something

Thanks for your help

.close

[cedar kiln]

Channel closed

Closed by @warm vector

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[gentle lintel]

hi

[gentle lintel]

i believe i’ve completed single variable calculus, but i’m not sure how to assess it

any suggested methods (except for khan academy)

[crimson sedge]

3b1b?

[gentle lintel]

i watched that during learning

[bold vine]

Are you comfortable with taking limits, derivatives, integrals, sequences and series? How comfortable do you feel with each of the topics taught in it?

[gentle lintel]

as a whole, not quite

[hollow osprey]

sequences and series r calc 2

[bold vine]

I’d argue it all lies in comfort. If you feel comfortable enough (for your own standard) with the concepts, then you should be good 🙂

[flint plinth]

If you want to be formally assessed, I think you can take the AP calculus test without actually taking a class.

[bold vine]

Correct

[hollow osprey]

oh my b he said single variable

[crimson sedge]

Yup

[bold vine]

This is one way

[hollow osprey]

i read calc 1

[bold vine]

Oh hehe np np

[gentle lintel]

i did that

[flint plinth]

Ah cool, how did you do?

[gentle lintel]

but i’m still shaky in terms of proceeding

[bold vine]

You can use Paul’s Online Math Notes

[gentle lintel]

i haven’t done them per se but i know how to do the questions

[gentle lintel]

i used that

during learning

[flint plinth]

Ah, got it

[hollow osprey]

well he didn't take the real ap test

that's in may

[gentle lintel]

much like 3b1b, much like khan academy

[bold vine]

Is there a reason you’d like to assess it?

[flint plinth]

You can always proceed with the next level of calculus and see how it goes. Subsequent classes build on the previous ones, so you get more practice and can quickly see where you are shaky

[gentle lintel]

i’m not sure whether i’m good to proceed

[gentle lintel]

i don’t plan on doing calculus just yet

i plan to do linear algebra

[hollow osprey]

linear alg is harder than calc 3

so you should do calc 3 first

[gentle lintel]

which, by the time i finish i believe my understanding will be uhh

[hollow osprey]

then lin alg

[gentle lintel]

not as good

[flint plinth]

Well linear algebra won't involve any calculus except perhaps for examples of linear maps

However, multivariable calculus (if taught correctly) will definitely use linear algebra!

[bold vine]

I found linear algebra easier than multi variable - likely because courses are shorter and don’t cover as much

[gentle lintel]

which is why i plan to do it first

[flint plinth]

Makes sense

[hollow osprey]

not the same level of rigor however

as a linear alg class that's interested in proving really everything it shows you

[flint plinth]

You could always do some other course that uses calculus to get some more practice, maybe classical mechanics in physics?

Or perhaps probability

[gentle lintel]

i don’t plan to study a whole field of physics just to ‘test my understanding’ lol

[hollow osprey]

yeah we learned before that chromium doesn't like physics lol

[flint plinth]

Sure, just throwing out some ideas, in case you were interested in any of those fields anyway

Best way to solidify calculus is to use it, IMO

[gentle lintel]

i don’t dislike them lol i just don’t want spoilers

[hollow osprey]

you wanted a reason for understanding something and you said "no physics allowed"

then was disappointed when there was no answer lol

[dire geode]

Take a final exam and time yourself. We'll grade you

[bold vine]

To solidify calculus: do lots of practice problems - not necessarily at once - but spread out - active recalling

[gentle lintel]

i think physical examples are too generic

[hollow osprey]

you mean specific?

[gentle lintel]

and overused in terms of conceptual explanations

[hollow osprey]

hence why i said you didn't like physics

[gentle lintel]

no like physics, yea nice examples and all

i was looking for other examples etc

[bold vine]

Physics is a unique “flavor” of math

[dire geode]

If you can't do generic examples what makes you think you can do harder ones

[hollow osprey]

https://sites.math.washington.edu/~m125/Quizzes/week10/125finalA21.pdf

[gentle lintel]

where can i find those

[hollow osprey]

this is a good final exam

if you wanna test urself

[bold vine]

That is a great final - nice

Covers just about everything

[hollow osprey]

ikr

i think its for only one quarter though

124 (calc 1 w/ no integrals) was 1 quarter (8 weeks) anyways

[flint plinth]

And even that final has some physics in it, nice 😁 - see problem 5

[dire geode]

https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/final-exam/

Another good one

[hollow osprey]

i never understood work

Work = force * distance

but like always setting it up was confusing

[bold vine]

I think it’s defined as a dot product and then simplified for specific directions

[hollow osprey]

makes sense

i need to watch a vid on it if i wanted to really understand it

[flint plinth]

It definitely seems like a misnomer, if I shove a heavy box down the hall and then back, I damn well did some work regardless of what the formula says.

[hollow osprey]

true

Lol

[bold vine]

That’s what it feels like, right?

[dire geode]

Even I would have a hard time doing this in 3-4 hours. Jesus christ it's long

[bold vine]

Unfortunately science doesn’t necessarily agree with what we perceive

Work ≠ what we would call “effort”

[hollow osprey]

17 pages!???

[flint plinth]

Yep, I have no problem with the concept of course, it just seems a bit odd to call it "work". But I'm long used to it by now, I'm just being facetious about my complaint

[bold vine]

Understandable

[flint plinth]

Those 2/3 of MIT freshmen aren't going to weed themselves out!

[dire geode]

Brutal

[hollow osprey]

it is

[flint plinth]

Assuming the old story about "look to your left, look to your right" was actually true

Then again at Harvard there's Math 55, where they laugh at ordinary calculus and other ordinary undergraduate courses.

[hollow osprey]

55 is real/complex analysis right?

[dire geode]

New problem on an MIT final. If everyone sits in a classroom with 30 rows and 30 columns, and everyone's told to look to their neighbors and only one of you three will remain, how many therapists in Cambridge will get overwhelmed with new patients.

[wraith crypt]

woah are we proctoring now

[flint plinth]

Yeah, there's also some abstract algebra

[hollow osprey]

oh jeez

[dire geode]

I think Chromi scammed us into doing grading for free

[wraith crypt]

a few years ago a few undergrads decided to ask my group for practice papers

we basically set three papers in 24 hours

[dire geode]

Have met grad students and professors who've taken Math 55. It's intense

[hollow osprey]

set three papers?

i like \text{} instead of \mathrm{}

[wraith crypt]

LOL

[wraith dagger]

riemann